Summary

DescriptionTime series of the Tent map for the parameter m=2.0 made with increased precision.svg	English: Time series of the Tent map for the parameter m=2.0 made with increased precision
Date	30 June 2019
Source	Own work
Author	Adam majewski
Other versions	Numerical errors for 16 digits of precision
SVG development InfoField	The SVG code is valid.   This chart was created with Gnuplot.    This plot uses embedded text that can be easily translated using a text editor.

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Maxima CAS src code

/* 


https://math.stackexchange.com/questions/2453939/is-this-characteristic-of-tent-map-usually-observed
*/

kill(all);
remvalue(all);
ratprint:false; /* a message informing the user of the conversion of floating point numbers to rational numbers is displayed. */
display2d:false;


/* ---------- functions ---------------------------------------------------- */



/* https://en.wikipedia.org/wiki/Tent_map */

f(x) :=	if x<0.5  then m*x else m*(1-x) $
	
	
	
GivePoints(x0, iMax):= block(
	[Points,i,Point],
	i:0,
	x:x0,
	Point:[i,x],
	Points:[Point],
	while (i<iMax)
    	do
    	( 
    		x:f(x),
    		i:i+1,
    		Point:[i,x],
    		Points:endcons(Point, Points)
    	 	
    	),
    	return(Points) 
	


)$

/* const */
m: bfloat(2.0);	
iMax:100;


fpprec:5+round(iMax/3.6); /* the number of stored decimal digits will be equal to the current value of */
fpprintprec:fpprec;
bftrunc:false;

x0:bfloat(random(10^fpprec) / 10^fpprec) ; /*Robert Dodier : https://stackoverflow.com/questions/56826546/how-to-compute-random-bfloat-number-in-maxima-cas */ 
/*x0:  bfloat(%pi)/6.0b0; */
Points:GivePoints(x0,iMax);




/* ------- draw --------------------------------------- */
load(draw);
path:"~/maxima/batch/tent/bf/bf2/"$ /*  pwd, if empty then file is in a home dir , path should end with "/" */


draw2d(
  user_preamble="set key top right; unset mouse; ",
  terminal  = 'svg,
  file_name = sconcat(path,"p", string(fpprec),"_", string(float(x0))),
  font_size = 20,
  font = "Liberation Sans", /* https://commons.wikimedia.org/wiki/Help:SVG#Font_substitution_and_fallback_fonts */
  title= sconcat("Time series of the Tent map for the parameter m=2.0 made with ", string(fpprec), " decimal digits"),
  xlabel     = "iteration ",
  ylabel     = "x",
  dimensions = [1000, 1000],
  yrange=[0,1],
  color= blue,
  point_type = filled_circle,
  point_size    =  0.2,
  points_joined =true,
  key = "",
  points(Points)
  
  
  
  )$